A custodian is struggling to move a 100. kg desk on a dolly, using a rope. He is pulling on the rope at a 60. ◦ angle. (a) How much force will the custodian need to apply in order to cause the desk to accelerate horizontally at a rate of 1.0 m s 2 ? (b) You suggest that the custodian will have an easier time if he uses a longer rope, which will decrease the angle. If the longer rope results in an angle of 30. ◦ , much force will the custodian need to apply in order to cause the 100. kg desk to accelerate horizontally at 1.0 m s 2 ?

We can solve this problem by applying Newton's second law: in fact, the net force along the horizontal direction must be equal to the product between the mass of the desk and the horizontal acceleration. Mathematically,

[tex]F_x = ma_x[/tex]

where

[tex]F_x = F cos \theta[/tex] is the net force on the horizontal direction, with F being the magnitude of the force applied by the custodian, and

[tex]\theta=60^{\circ}[/tex] the angle at which the force is applied

m is the mass of the desk

[tex]a_x[/tex] is the horizontal acceleration

In this problem we have:

m = 100 kg

[tex]a_x = 1.0 m/s^2[/tex]

Solving for F, we find the force that the custodian must apply:

[tex]F=\frac{ma_x}{cos \theta}=\frac{(100)(1.0)}{cos 60^{\circ}}=200 N[/tex]

b)

In this case, the rope has an angle of [tex]30^{\circ}[/tex] with the horizontal: this means that the force is applied at an angle of

[tex]\theta=30^{\circ}[/tex]

with the horizontal.

As before, we can apply Newton's second law:

[tex]F_x = ma_x[/tex]

And we have again

m = 100 kg (mass of the desk)

[tex]a_x=1.0 m/s^2[/tex] (horizontal acceleration)

This can be rewritten as

[tex]Fcos \theta = ma_x[/tex]

And solving for F, we find

[tex]F=\frac{ma_x}{cos \theta}=\frac{(100)(1.0)}{cos 30^{\circ}}=115.4 N[/tex]

Learn more about Newton's second law:

brainly.com/question/3820012

#LearnwithBrainly